Dear James,
How long are the sticks? What is the definition of RELATIVE APPARENT
SYNAPOMORPHY? For short sticks (L < 25 cm) the only way three squares can
share a stick is if two of them share a corner and each of the two shares an
edge with the third. For medium sticks (25 cm < L < ~56 cm) the squares can
also be three in a row. For long sticks ( L > ~56 cm) two squares cannot
share a stick to the exclusion of a third. Comparisons of the SIGMA RAP
scores with the equivalent three-square measure might allow the recipient to
determine whether the sticks were short or medium, and if medium, how long
they were (based on the ratio of three-in-a-row to three-in-an-L). In all
cases where i, j, and k share a stick, the SIGMA RAP cannot be non-zero for
all three pairs, assuming that no stick lands precisely on a corner of a
square or that the sticks have a finite width.
Yours,
Bill Tivol